We argue that the recently reported Kolmogorov-like magnetic turbulence spectrum in the cool core of the Hydra A galaxy cluster can be understood by kinetic energy injection by active galaxies that drives a turbulent non-helical magnetic dynamo into its saturated state. Although dramatic differences exist between small-scale dynamo scenarios, their saturated state is expected to be similar, as we show for three scenarios: the flux rope dynamo, the fluctuation dynamo, and the explosive dynamo. Based on those scenarios, we develop an analytical model of the hydrodynamic and magnetic turbulence in cool cores. The model implies magnetic field strengths that fit well with Faraday rotation measurements and minimum energy estimates for the sample of cool core clusters having such data available. Predictions for magnetic fields in clusters for which the appropriate observational information is still missing, and for yet unobserved quantities like the hydrodynamical turbulence velocity and characteristic length-scale are provided. The underlying dynamo models suggest magnetic intermittency and possibly a large-scale hydrodynamic viscosity. We conclude that the success of the model to explain the field strength in cool core clusters indicates that in general cluster magnetic fields directly reflect hydrodynamical turbulence, also in clusters without cool cores.
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